Given that ABCD is a rhombus with ADC = 120 degrees, and AD = 8 cm, OE = 2√2, and BD = 4 cm, we need to find the value of AE.
Since ABCD is a rhombus, all sides are equal in length. Therefore, BD = AD = 8 cm.
In triangle ABD, using the Law of Cosines, we haveAB^2 = AD^2 + BD^2 - 2ADBDcos(ADBAB^2 = 8^2 + 4^2 - 284cos(120AB^2 = 64 + 16 - 64*(-0.5AB^2 = 64 + 16 + 3AB^2 = 11AB = √11AB = 4√7
Since AE is the same length as AB, AE = 4√7 + OAE = 4√7 + 2√AE = 2√7 + 8
Therefore, the length of AE is 2√7 + 8 cm.
Given that ABCD is a rhombus with ADC = 120 degrees, and AD = 8 cm, OE = 2√2, and BD = 4 cm, we need to find the value of AE.
Since ABCD is a rhombus, all sides are equal in length. Therefore, BD = AD = 8 cm.
In triangle ABD, using the Law of Cosines, we have
AB^2 = AD^2 + BD^2 - 2ADBDcos(ADB
AB^2 = 8^2 + 4^2 - 284cos(120
AB^2 = 64 + 16 - 64*(-0.5
AB^2 = 64 + 16 + 3
AB^2 = 11
AB = √11
AB = 4√7
Since AE is the same length as AB, AE = 4√7 + O
AE = 4√7 + 2√
AE = 2√7 + 8
Therefore, the length of AE is 2√7 + 8 cm.